Charge is uniformly distributed on the surface of a hollow hemisphere. Let $O$ and $A$ be two points on the base of the hemisphere and $V_0$ and $V_A$ be the electric potentials at $O$ and $A$ respectively. Then,
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A resistance $R$ and a capacitance $C$ are connected in series to a battery of negligible internal resistance through a key. The key is closed at $t = 0$. If after $t\, sec$ the voltage across the capacitance was seven times the voltage across $R$, the value of $t$ is
$2\,\mu F$ capacitance has potential difference across its two terminals $200\;volts$. It is disconnected with battery and then another uncharged capacitance is connected in parallel to it, then $P.D.$ becomes $20\;volts$. Then the capacity of another capacitance will be.......$\mu F$
A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V\ volt$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
A capacitor of capacitance $\mathrm{C}$ and potential $\mathrm{V}$ has energy $E$. It is connected to another capacitor of capacitance $2 \mathrm{C}$ and potential $2 \mathrm{~V}$. Then the loss of energy is $\frac{x}{3} E$, where $\mathrm{x}$ is____________.
Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is
The electric potential $V$ at any point $(x, y, z),$ all in metres in space is given by $V = 4x^2$ volt. The electric field at the point $(1, 0, 2)$ in volt/meter, is
A spherical metal shell $A$ of radius $R_A$ and a solid metal sphere $B$ of radius $R_B\left( < R_A\right)$ are kept far apart and each is given charge ' $+Q$ '. Now they are connected by a thin metal wire. Then
A parallel plate air capacitor is charged to a potential difference of $V\, volts$. After disconnecting the charging battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result, the potential difference between the plates